A highly concentrated ammonia solution is found to have a pH of 12.19 M. What is the hydroxide concentration, #["OH"^(-)(aq)]# in #"mol L"^-1#?

1 Answer
zhirou
May 26, 2018

#1.5 xx 10^-2 M#.

Explanation:

To answer this question, we'll need to use these two formulas:

  • #pH = -log[H^+]#
  • #[H^+]xx[OH^-] = 1.0xx10^(-14)# (at #25 ºC#)

The question tells us that our solution has a #pH# of #"12.19 M"#.
So, we can use the first formula to find the molar concentration of #H^+# ions:

#pH = -log[H^+]#
#"12.19" = -log[H^+]#
#10^(-"12.19") = [H^+]#
#6.5 xx 10^(-13) M = [H^+]#

(The concentration of #H^+# has #2# significant figures because the number of significant figures in the concentration equals the number of decimal places in the #pH#.)

Now that we know the molar concentration of #H^+#, we can use the second formula to find the molar concentration of #OH^-# (if we assume that the temperature of the solution was #25ºC#):

#[H^+]xx[OH^-] = 1.0xx10^(-14)#
#[OH^-] = (1.0xx10^(-14))/([H^+])#
#[OH^-] = (1.0xx10^(-14))/(6.5 xx 10^(-13))#
#[OH^-] = 1.5 xx 10^-2 M#

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